В треугольнике со сторонами: a = 18.19, b = 10.5, с = 21, углы равны α° = 60°, β° = 30°, γ° = 90°
Ответ:
a=18.19
b=10.5
c=21
α°=60°
β°=30°
γ°=90°
S = 95.62
ha=10.51
hb=18.21
hc=9.107
P = 49.69
Решение:
Сторона:
b = c·
sin(β°)
sin(γ°)
= 21·
sin(30°)
sin(90°)
= 21·
0.5
1
= 21·0.5
= 10.5
Угол:
α° = 180 - γ° - β°
= 180 - 90° - 30°
= 60°
Сторона:
a = √b2 + c2 - 2bc·cos(α°)
= √10.52 + 212 - 2·10.5·21·cos(60°)
= √110.25 + 441 - 441·0.5
= √330.75
= 18.19
или:
a = b·
sin(α°)
sin(β°)
= 10.5·
sin(60°)
sin(30°)
= 10.5·
0.866
0.5
= 10.5·1.732
= 18.19
или:
a = c·
sin(α°)
sin(γ°)
= 21·
sin(60°)
sin(90°)
= 21·
0.866
1
= 21·0.866
= 18.19
Периметр:
P = a + b + c
= 18.19 + 10.5 + 21
= 49.69
Площадь:
p =
a + b + c
2
S =√p·(p-a)·(p-b)·(p-c)
=√24.85·(24.85-18.19)·(24.85-10.5)·(24.85-21)
=√24.85 · 6.66 · 14.35 · 3.85
=√9143.5164975
= 95.62
Высота :
ha =
2S
a
=
2 · 95.62
18.19
= 10.51
hb =
2S
b
=
2 · 95.62
10.5
= 18.21
hc =
2S
c
=
2 · 95.62
21
= 9.107